Lesson 7.2 Finding Critical Features of Quadratic Equations

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Presentation transcript:

Lesson 7.2 Finding Critical Features of Quadratic Equations Objective - To algebraically find critical features of parabolic curves. Quadratic Equation Quadratic Term Linear Term Constant Term a c opens up y-intercept +a -a opens down shifts up +c skinny parabola shifts down -c wide parabola Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

Finding Critical Features of Quadratics Graph Axis x=3 x y y has no maximum x y -3 -2 -1 1 2 3 29 18 10 x has no mimimum x has no maximum 2 -3 -6 Vertex Minimum Value (3,-7) -7 y = -7 4 5 -6 -3 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Finding Critical Features of Quadratics Vertex Axis of Symmetry Opens Up/Down Opens Up Y-intercept (0, 2) Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Find the critical features of the quadratic below. Vertex Axis of Symmetry Opens Up/Down Opens Down Y-intercept (0, 0) Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Find the critical features of the quadratic below. Vertex Axis of Symmetry Opens Up/Down Opens Up Y-intercept (0, 4) Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

and then find the critical features of the quadratic algebraically. Graph x y x y -3 -2 -1 1 2 3 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

and then find the critical features of the quadratic algebraically. Graph x y Axis Vertex (1,9) Vertex x = 1 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

and then find the critical features of the quadratic algebraically. Graph Y-int.= 8 y-intercept Vertex x y (1,9) Opens Up/ Down? Max. or Min Value x = 1 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series